Theorem mulcomi 7765

Description: Commutative law for multiplication. (Contributed by NM, 23-Nov-1994.)

Hypotheses

Ref	Expression
axi.1	|- A e. CC
axi.2	|- B e. CC

Assertion

Ref	Expression
mulcomi	|- ( A x. B ) = ( B x. A )

Proof of Theorem mulcomi

Step	Hyp	Ref	Expression
1		axi.1	. 2 |- A e. CC
2		axi.2	. 2 |- B e. CC
3		mulcom 7742	. 2 |- ( ( A e. CC /\ B e. CC ) -> ( A x. B ) = ( B x. A ) )
4	1, 2, 3	mp2an 422	1 |- ( A x. B ) = ( B x. A )

Syntax hints:   = wceq 1331   e. wcel 1480  (class class class)co 5767   CCcc 7611   x. cmul 7618

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 107  ax-mulcom 7714

This theorem is referenced by:  mulcomli  7766  8th4div3  8932  numma2c  9220  nummul2c  9224  9t11e99  9304  binom2i  10394  fac3  10471  tanval2ap  11409  sincosq4sgn  12899